Abstract : The adaptive, self-learning, and superior analytical capabilities of neural networks for nonlinear systems make them a commonly used method for fault diagnosis. This paper analyzes the structure and characteristics of RBF neural networks, using the deformation measured by sensors at key locations on a tower crane as feature parameters, and applies RBF neural networks to diagnose and analyze typical faults in tower cranes. Practice shows that the RBF neural network method is effective and feasible for fault diagnosis of multi-symptom mechanical systems. Keywords : RBF neural network; tower crane; fault diagnosis 0 Introduction Based on the different information generated by tower cranes in different states, the operating state of a tower crane deviating from normal operation is called a fault state. As can be seen from the principle of fault diagnosis, the fault diagnosis process is the nonlinear mapping of a set of fault symptoms to a set of faults. A certain type of fault in the diagnosed equipment often causes multiple fault symptoms; a certain fault symptom can be caused by multiple fault types. Therefore, essentially, the fault diagnosis process is a classification and identification process. This process is difficult to describe with a clear mathematical model; the use of neural networks makes this classification and identification possible. Neural networks, as a novel methodological system, possess characteristics such as distributed parallel processing, nonlinear mapping, adaptive learning, and robust fault tolerance, making them widely applicable in pattern recognition, control optimization, intelligent information processing, and fault diagnosis. Currently, commonly used neural network models include Adaptive Resonance Theory (ART), Backpropagation Error (BP), Self-Organizing Map (SOM), and Radial Basis Function (RBF) models, with BP and RBF models being the most widely used. This paper analyzes the structure and characteristics of the RBF neural network model, using the deformation measured by sensors at key locations on a tower crane as feature parameters, and applies the RBF neural network to diagnose and analyze seven typical faults of tower cranes. Experimental results show that using the RBF neural network is effective and feasible for diagnosing faults in multi-symptom mechanical systems. [b]1 RBF Neural Network Model[/b] The BP network is a typical global approximation network, meaning that all parameters of the network must be adjusted for each input and output data. Because BP neural networks learn using the gradient descent-based error backpropagation algorithm, their training speed is usually slow, and they are prone to getting stuck in local minima. Although some improved fast algorithms can solve certain practical problems better, the design process often involves repeated trial and error and training, making it impossible to strictly guarantee the convergence and global optimality of the BP algorithm in each training session. Furthermore, the working mechanism and number of hidden neurons in BP networks are also difficult problems to determine. Radial basis function (RBF) networks, on the other hand, are a type of feedforward network constructed based on function approximation theory. Learning in this type of network is equivalent to finding the best-fit surface for the training data in a multi-dimensional space. The transfer function of each hidden neuron in the network constitutes a basis function of the fitting plane. RBF networks are a type of local approximation network, where only a few neurons are used to determine the network's output for a certain local region of the input space. Due to their fundamentally different constructions, RBF networks are usually larger in scale than BP networks, but they learn faster, and their function approximation ability, pattern recognition, and classification ability are superior. 1.1 RBF Neuron Model A radial basis function neuron model with 3D input is shown in Figure 1. The module in the figure represents the distance between the input vector and the weight vector. In this model, the Gaussian function radbas is used as the transfer function of the radial basis function (RBF) neuron. Its input is the distance between the input vector and the weight vector w multiplied by a threshold. The Gaussian function radbas is a typical radial basis function, and its expression and function curve are shown in Figure 2. [align=center] Figure 1 Radial basis function neuron with R-dimensional input[/align] [align=center] Figure 2 Gaussian radial basis function curve[/align] Center and width are two important parameters of the radial basis function neuron. The weight vector w of the neuron determines the center of the radial basis function. When the input vector coincides with w, the output of the radial basis function neuron reaches its maximum value. The farther the input vector is from w, the smaller the output of the neuron. The threshold of the neuron determines the width of the radial basis function. The larger the threshold, the greater the decay of the function as the input vector moves away from w. 1.2 RBF Neural Network Structure A typical radial basis function network consists of two layers: a hidden layer and an output layer, as shown in Figure 3. The input dimension of the network is , the number of hidden layer neurons is , and the number of outputs is . The hidden layer neurons use Gaussian function as transfer function, and the transfer function of the output layer is linear function. In the figure, represents the element of the hidden layer output vector, and represents the weight vector of the hidden layer neuron, that is, the i-th row of the hidden layer neuron matrix w. [align=center] Figure 3 Radial basis function network structure diagram[/align] 2 Examples of common fault diagnosis of tower cranes After extensive field investigation and analysis, the main typical faults of tower cranes are: (1) excessive lifting capacity (A); (2) insufficient tower crane rigidity (B); (3) large lifting torque (C); (4) large lifting height (D); (5) inappropriate lifting amplitude (E); (6) high wind speed (F); (7) loose support points (G). By conducting field tests on the faults of tower cranes, the deformation at the key position of the tower is measured by the sensor installed on the tower body, and the status of the tower crane is monitored by the data acquisition system and the data processing system. A total of 9 test points are selected as the detection objects. Data was collected for each fault state to form standard sample data and data to be tested. The collected sample data was normalized, and an RBF network was designed using an iterative method to train 70 training samples (10 of each type) to make the network training more effective. This method adds one neuron per iteration until the sum of squares error drops below the target error, at which point the iteration stops. In the network settings, the target error was 0.01, and the expansion constant was 0.5. The network training process is shown in Figure 4. [align=center] Figure 4 RBF Neural Network Training Process[/align] The training process shows that the RBF algorithm reached the target error requirement in 15 iterations, which is much faster than the BP algorithm, which often requires hundreds or thousands of iterations. 3 Experimental Results To verify the diagnostic performance of the trained RBF neural network for tower crane faults, this paper uses MATLAB for experimental simulation. The detection results are shown in Table 1 (3 sets of samples to be tested), fed into the trained RBF network, and the detection results are shown in Table 2. Table 1 Test Samples Table 2 Network Diagnostic Output Results As can be seen from the bold numbers in Table 2, the RBF network can effectively diagnose the three situations. The results show that the RBF network has a unique solution, does not have the local minima problem encountered by the BP network, and unlike the slow convergence speed of the BP network, the RBF network has a fast learning speed, making it suitable for online real-time monitoring and diagnosis. [b]4 Conclusion[/b] This paper studies a fault diagnosis method for tower cranes based on RBF neural networks. Based on summarizing the fault patterns of tower cranes, the neural network toolbox functions of MATLAB are used to train and simulate the network to realize fault diagnosis of tower cranes. Simulation examples of test samples show that the method is effective and feasible.